Internal problem ID [2285]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 35, page 157
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y^{\prime \prime }-{y^{\prime }}^{2}=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)=1+diff(y(x),x)^2,y(x), singsol=all)
\[ y \left (x \right ) = -\ln \left (\frac {c_{1} \tan \left (x \right )-c_{2}}{\sec \left (x \right )}\right ) \]
✓ Solution by Mathematica
Time used: 1.736 (sec). Leaf size: 16
DSolve[y''[x]==1+y'[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2-\log (\cos (x+c_1)) \]